To construct a model for a second-order topological superconductor protected by fourfold rotation symmetry [1]}, [2]}, we consider a square lattice in the \(xy\)  plane and place at each lattice site a Majorana mode \(\gamma _i = \gamma _i^\dagger \) .
We add imaginary nearest-neighbor hopping between the Majorana modes, which we dimerize in the \(x\)  and in the \(y\)  direction.
Finally, we thread a magnetic flux quantum through each lattice plaquette.
The model is illustrated in Fig. REF (a).
It can be viewed as an array of alternatingly coupled Kitaev chains in the presence of a gauge field.
The Bloch Hamiltonian of the model reads
\(H_{\mathrm {D},4}(\mathbf {k}) &=& (t+\delta t)\,[\tau _3\rho _2 + \tau _2\rho _0]\nonumber \\&& -(t-\delta t)\,[\cos (k_x)\tau _3\rho _2 + \sin (k_x)\tau _3\rho _1]\nonumber \\&& -(t-\delta t)\,[\cos (k_y)\tau _2\rho _0 + \sin (k_y)\tau _1\rho _0],\) 
